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Design optimization of laminated composite plates with static and dynamic considerations in hygrothermal environments

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Abstract

Motivated by needs such as those in the aerospace industry, this paper develops and demonstrates a method for optimizing laminated composite shell components considering the natural frequency, damping and deflection subjected to a concentrated load on the center of the plate in hygrothermal environments by manipulating individual ply angles and thicknesses. Optimization is performed by synergizing an FEA with a gradient-based modified feasible direction optimization algorithm. The objective is to minimize the weight of the plates within the given design space via the constraint of the first natural frequency, dampings of the first vibration modes and deflections caused by the applied hygro-thermo-mechanical loads. Illustrative applications involve six-ply symmetric rectangular laminated panels simply supported along four edges, although the method is applicable to more complicated laminates, geometries and boundary conditions. The panel geometry is discretized into specially-developed, 3D-degenerated eight-node shell isoparametric layered composite elements. Through a numerical example, it is shown that hygro-thermal effects play an important role in the optimal design of laminated composites.

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Abbreviations

er, es, et :

shell element directional unit vectors

N k :

shape function

V kn :

normal vector to the shell mid-surface

[C sh ]:

shell element material stiffness matrix

[T sh ]:

shell element transformation matrix

α xx :

x-direction thermal expansion coefficient

β xx :

x-direction hygro coefficient

R I :

thermally induced equivalent nodal force

ɛ th :

thermal strain

ɛ hy :

hygro strain

Ψ :

damping capacity

U e :

total strain energy

[K s ]:

static stiffness matrix

[K th ]:

temperature stiffness matrix

[K hy ]:

moisture stiffness matrix

[B]:

strain-displacement matrix

[M]:

mass matrix

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  1. Department of Mechanical Engineering Education, Andong National University, 1375 Gyeongdong-ro, Andong-si, Gyeongsangbuk-do, South Korea, 760-749

    Hee-Keun Cho

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Cho, HK. Design optimization of laminated composite plates with static and dynamic considerations in hygrothermal environments. Int. J. Precis. Eng. Manuf. 14, 1387–1394 (2013). https://doi.org/10.1007/s12541-013-0187-7

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  • DOI: https://doi.org/10.1007/s12541-013-0187-7

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